No full-text available
To read the full-text of this research,
you can request a copy directly from the author.
Proof of Concept and dose estimation with binary responses under model uncertainty
Abstract
This article suggests a unified framework for testing Proof of Concept (PoC) and estimating a target dose for the benefit of a more comprehensive, robust and powerful analysis in phase II or similar clinical trials. From a pre-specified set of candidate models, we choose the ones that best describe the observed dose-response. To decide which models, if any, significantly pick up a dose effect, we construct the permutation distribution of the minimum P-value over the candidate set. This allows us to find critical values and multiplicity adjusted P-values that control the familywise error rate of declaring any spurious effect in the candidate set as significant. Model averaging is then used to estimate a target dose. Popular single or multiple contrast tests for PoC, such as the Cochran-Armitage, Dunnett or Williams tests, are only optimal for specific dose-response shapes and do not provide target dose estimates with confidence limits. A thorough evaluation and comparison of our approach to these tests reveal that its power is as good or better in detecting a dose-response under various shapes with many more additional benefits: It incorporates model uncertainty in PoC decisions and target dose estimation, yields confidence intervals for target dose estimates and extends to more complicated data structures. We illustrate our method with the analysis of a Phase II clinical trial.
... We assumed a true CR of 5%, 10%, 20%, 30%, and 40% against T. trichiura and a loss to follow-up of 5%. We estimated that enrolling 40 participants per arm will be sufficient to predict the dose response curve with a precision of about 10% points [16]. See supplementary material for details in sample size determination. ...
... The findings of this trial are comparable to others on albendazole in the literature. In a recent network meta-analysis, Moser and colleagues found that 400 mg of albendazole had a limited efficacy against T. trichiura with CRs having decreased from 38¢6% in 1999 to 16.4% in 2015 [10]. However, most of the trials included in the analysis limited their study populations to SAC [10]. ...
Background
The efficacy of the widely used albendazole against the soil-transmitted helminth Trichuris trichiura is limited; yet optimal doses, which may provide increased efficacy, have not been thoroughly investigated to date.
Methods
A randomized-controlled trial was conducted in Côte d'Ivoire with preschool-aged children (PSAC), school-aged children (SAC), and adults infected with T. trichiura. Participants were randomly assigned (1:1:1:1) using computer-generated randomization. PSAC were randomized to 200 mg, 400 mg, 600 mg of albendazole or placebo. SAC and adults were randomized to 400 mg, 600 mg, 800 mg of albendazole or placebo. The primary outcome was cure rates (CRs) against trichuriasis. Secondary outcomes were T. trichiura egg reduction rates (ERRs), safety, CRs and ERRs against other soil-transmitted helminths. Outcome assessors and the trial statistician were blinded. Trial registration at ClinicalTrial.gov: NCT03527745.
Findings
111 PSAC, 180 SAC, and 42 adults were randomized and 86, 172, and 35 provided follow-up stool samples, respectively. The highest observed CR among PSAC was 27·8% (95% CI: 9·7%–53·5%) in the 600 mg albendazole treatment arm. The most efficacious arm for SAC was 600 mg of albendazole showing a CR of 25·6% (95% CI: 13·5%–41·2%), and for adults it was 400 mg of albendazole with a CR of 55·6% (95% CI: 21·2%–86·3%). CRs and ERRs did not differ significantly among treatment arms and flat dose-responses were observed. 17·9% and 0·4% of participants reported any adverse event at 3 and 24 h follow-up, respectively.
Interpretation
Albendazole shows low efficacy against T. trichiura in all populations and doses studied, though findings for PSAC and adults should be carefully interpreted as recruitment targets were not met. New drugs, treatment regimens, and combinations are needed in the management of T. trichiura infections.
Funding
Bill and Melinda Gates Foundation.
... The actual functional form of a dose-response relationship is not essential if the distribution of responses can be determined for any dose, although it would be important when the objective is to characterize a dose-response relationship based on pharmacokinetic or pharmacodynamic models and principles. A number of approaches address model specification uncertainty when the possibility that the model used in a model-based approach might be incorrect (Bornkamp, Bretz, Dette, & Pinheiro, 2011;Bretz, Pinheiro, & Branson, 2005;Dette, Titoff, Volgushev, & Bretz, 2015;Faes et al., 2007;Klingenberg, 2009;Link & Albers, 2007;Morales et al., 2006;Ohlssen & Racine, 2015;Pinheiro, Bornkamp, & Bretz, 2006;Verrier, Sivapregassam, & Solente, 2014). It may be counterproductive to attempt to find a "best" functional form for a dose-response relationship: "…misspecifying the parametric model can lead to substantial bias in estimating the dose-response curve" (Dette et al., 2015). ...
... The calculations described below replace b 3 with 1/b 3 in the EMAX models and assume b 3 < 0 in the exponential model to improve computational stability. This certainly is not a complete list and many other models can be used, including fractional polynomials (Faes et al., 2007;Klingenberg, 2009;Ritz, Baty, Streibig, & Gerhard, 2015;Royston & Altman, 1994;Verrier et al., 2014), cubic splines (Crainiceanu, Ruppert, & Wand, 2005;Helms, Benda, Zinserling, Kneib, & Friede, 2015;Liu, Zhou, & Bretz, 2014), and various non-and semi-parametric models (Dette et al., 2015;Haaland & Chiang, 2014;Li & Fu, 2016;Ohlssen & Racine, 2015). The models do not need to be limited to monotonic functions of dose. ...
Successful pharmaceutical drug development requires finding correct doses. The issues that conventional dose‐response analyses consider, namely whether responses are related to doses, which doses have responses differing from a control dose response, the functional form of a dose‐response relationship, and the dose(s) to carry forward, do not need to be addressed simultaneously. Determining if a dose‐response relationship exists, regardless of its functional form, and then identifying a range of doses to study further may be a more efficient strategy. This article describes a novel estimation‐focused Bayesian approach (BMA‐Mod) for carrying out the analyses when the actual dose‐response function is unknown. Realizations from Bayesian analyses of linear, generalized linear, and nonlinear regression models that may include random effects and covariates other than dose are optimally combined to produce distributions of important secondary quantities, including test‐control differences, predictive distributions of possible outcomes from future trials, and ranges of doses corresponding to target outcomes. The objective is similar to the objective of the hypothesis‐testing based MCP‐Mod approach, but provides more model and distributional flexibility and does not require testing hypotheses or adjusting for multiple comparisons. A number of examples illustrate the application of the method.
... When dealing with binary responses, slightly different models and formulae apply, but the general methodology is the same. We have used the models proposed by Klingenberg [9] (see Table 4) and the R macros he proposed to calculate the contrasts, the model estimations, and the model selections. We have also used a recent generalization of the MCP-Mod approach which allows us to address non-normal data (Pinheiro et al. [10]) in order to compare the results. ...
... The set of pre-specified candidate models is presented in Table 4. In order to look at the stability of the conclusions and to compare the Klingenberg and the Pinheiro approaches, we show the results obtained with 10 and 5 models using Klingenberg's [9] method on the one hand and the results obtained with the 5 same models using the generalized MCP-Mod approach proposed by Pinheiro et al. [10] on the other. The results are presented in Table 5. ...
Background:
Phase II clinical trials are important milestones to determine whether a dose-effect exists and to decide on future doses to use in confirmatory studies. To take into account the overall shape of the dose-response curve, modeling the relationship by linear or non-linear models is preferable to the classical pair-wise comparisons of the effect of each dose versus the placebo or the comparator. The multiple comparisons and modeling approach has been developed within the last 10 years to address this important question in the clinical development of drugs. Despite some recent publications referring to this methodology, few detailed applications have been shown so far and several practical questions remain to be addressed.
Methods:
Starting from a set of candidate models, model selection using classical methods criteria is possible. However, it suffers some limitations, not taking into account the uncertainty of the selection process itself. An attractive solution is to use model averaging, which applies appropriate weights to the parameters (e.g., the minimum effective dose) obtained from each model.
Results:
A discussion of the selection criteria is first presented. Through two real examples, how to proceed with model selection and model averaging is presented and discussed.
Limitations:
The first multiple comparisons and modeling approach papers addressed normal responses. More recently, an extension of this methodology has been proposed to deal with other types of responses, in particular binary, time-to-event and longitudinal data. Questions that remain are concerned with the choice of the candidate models and of their parameters' guesstimates.
Conclusions:
The analysis of clinical dose-finding studies using a modeling of the entire curve offers a promising alternative as compared with the classical multiple comparisons methods, while not compromising the necessary rigor of the analysis.
... Assumed CRs against hookworm for placebo and albendazole at 200 mg, 400 mg, 600 mg, and 800 mg were 2.5%, 30%, 50%, 70%, and 80%, respectively, while loss to follow-up was estimated at 10%. Simulations indicated that 40 participants per arm would be sufficient to predict the dose-response curve with a median precision, defined as one-half the length of the corresponding confidence band of approximately 10 percentage points [22]. ...
Background:
Infections with hookworms affect about half a billion people worldwide. Recommended therapy includes 400 mg of albendazole, which is moderately efficacious. Higher doses have been rarely assessed.
Methods:
A randomized controlled dose-finding trial was conducted in a low transmission setting in Côte d'Ivoire aiming to recruit 120 preschool-aged children (PSAC), 200 school-aged children (SAC) and 200 adults. Eligible PSAC were randomized 1:1:1 to 200 mg, 400 mg, or 600 mg of albendazole, the other age groups 1:1:1:1:1 to placebo or 200 mg, 400 mg, 600 mg, or 800 mg. The primary outcome was cure rates (CRs) assessed 14-21 days post-treatment by quadruplicate Kato-Katz thick smears. Hyperbolic Emax models were used to determine dose-response.
Results:
38 PSAC, 133 SAC, and 196 adults were enrolled. In adults, predicted CRs increased with ascending doses of albendazole with a CR of 74.9% (95% Confidence Interval: 55.6%-87.7%) in the 800 mg arm. Observed CRs increased with ascending doses of albendazole and reached a maximum of 94.1% (95% CI: 80.3%-99.3%). In SAC, the predicted dose-response curve increased marginally with CRs ranging from 64.0% in the 200 mg to 76.0% in the 800 mg arm. Sample size in PSAC was considered too small to derive meaningful conclusions. Only 10.7% and 5.1% of participants reported any adverse event at 3 hours and 24 hours post-treatment, respectively.
Conclusions:
A single 800 mg albendazole dose provides higher efficacy against hookworm and is well tolerated in adults and should be considered for community-based strategies targeting adults. For PSAC/SAC, current recommendations suffice.
... 4,8,9 Extensions of the MCP-Mod procedure have been proposed in recent years. Klingenberg 10 proposed methods for PoC testing and target dosage estimation in the case of a binary outcome. Pinheiro et al 11 extended the MCP-Mod approach to general parametric models and general study designs. ...
In the process of developing drugs, proof‐of‐concept studies can be helpful in determining whether there is any evidence of a dose‐response relationship. A global test for this purpose that has gained popularity is a component of the multiple comparisons procedure with modeling techniques (MCP‐Mod), which involves the specification of a candidate set of several plausible dose‐response models. For each model, a test is performed for significance of an optimally chosen contrast among the sample means. An overall P‐value is obtained from the distribution of the maximum of the contrast statistics. This is equivalent to basing the test on the minimum of the P‐values arising from these contrast statistics and, hence, can be viewed as a method for combining dependent P‐values. We generalize this idea to the use of different statistics for combining the dependent P‐values, such as Fisher's combination method or the inverse normal combination method. Simulation studies show that the generalized multiple contrast tests (GMCTs) based on the Fisher and inverse normal methods are generally more powerful than the MCP‐Mod procedure based on the minimum of the P‐values except for cases where the true dose‐response model is, in a sense, near the extremes of the candidate set of dose‐response models. The proposed GMCTs can also be used for model selection and dosage selection by employing a closed testing procedure.
... The suggested sample size is also in line with the recommendations from Klingenberg in 2009. 26 To account for losses in the follow-up, the sample size was increased to 40 children in each study group. ...
Schistosomiasis is a wide-spread chronic neglected tropical disease prevalent mostly in children in under-resourced rural areas. Its pathological effects have been clinically characterized, yet the molecular-level effects are understudied. In this study, the biochemical effects of Schistosoma mansoni infection and praziquantel treatment were studied in 159 pre-school aged and 130 school aged infected children and 11 non-infected children in Azaguié, Côte d’Ivoire. Urine samples were collected prior to receiving 20, 40 or 60 mg/kg of praziquantel or a placebo, as well as 24 hours post-treatment, and at the 3-week follow up. Urinary metabolic phenotypes were measured using 1H NMR spectroscopy and metabolic variation associated with S. mansoni infection and praziquantel administration was identified using multivariate statistical techniques. Discriminatory metabolic signatures were detected between heavily infected and non-infected children at baseline as well as according to the dose of praziquantel administered 24 hours post treatment. These signatures were primarily associated with the metabolic activity of the gut microbiota, gut health and growth biomarkers and energy and liver metabolism. These analyses provide insights into the metabolic phenotype of schistosomiasis and treatment with praziquantel in two important demographics.
... The main aim of this study was to elucidate the dose-response relationship of ivermectin against T. trichiura. Computer simulations showed that with 40 children enrolled in each of the study arms (0, 200, 400, and 600 µg/kg or 0, 100, and 200 µg/kg ivermectin) the dose-response prediction model had a median precision (half of the 95% confidence interval [CI]) of 10%, assuming associated CRs of 2.5%, 30%, 50%, and 70% for 0, 200, 400, and 600 µg/kg ivermectin, respectively [31]. ...
Background:
Although trichuriasis affects millions of children worldwide, recommended drugs lack efficacy and new treatment options are urgently needed. Ivermectin has promising potential to complement the anthelminthic armamentarium.
Methods:
A randomized placebo-controlled trial was conducted in rural Côte d'Ivoire to provide evidence on the efficacy and safety of ascending oral ivermectin dosages in preschool-aged children and in schoolchildren infected with Trichuris trichiura. Primary outcome was cure rate on T. trichiura infection and secondary outcomes were safety, egg-reduction rates against T. trichiura infection, and cure and egg-reduction rates against other soil-transmitted helminth species.
Results:
126 preschool-aged and 166 school-aged children were included in an available case analysis. In preschool-aged children efficacy against T. trichiura did not differ between 200 µg/kg ivermectin and placebo as expressed in cure rates (20.9% [95% CI 11.9-52.8%] vs. 19.5% [95% CI 10.4-49.9%]) and geometric mean egg-reduction rates (78.6% [95% CI 60.1-89.5%] vs. 68.2% [95% CI 40.5 to 84.8%]). In school-aged children even a dose of 600 µg/kg ivermectin revealed a low cure rate (12.2% [95% CI 4.8-32.3%] and moderate egg-reduction rate (66.3% [95% CI 43.8-80.2%]. Only mild adverse events and no organ toxicity based on serum biomarkers was observed.
Conclusion:
Ivermectin can be administered safely to preschool-aged children suffering from trichuriasis. Given the low efficacy of ivermectin monotherapy against T. trichiura infection further research should investigate the optimal drug combinations and dosages with ivermectin against soil-transmitted helminthiasis.
Trial registration:
The trial is registered at www.isrctn.com, number ISRCTN15871729.
... The suggested sample size is also in line with the recommendations from Klingenberg in 2009. 26 To account for losses in the follow-up, the sample size was increased to 40 children in each study group. ...
Background
Praziquantel has been the drug of choice for schistosomiasis control for more than 40 years, yet surprisingly, the optimal dose for children younger than 4 years is not known. We aimed to assess the efficacy and safety of escalating praziquantel dosages in preschool-aged children (PSAC).
Methods
We did a randomised controlled, parallel-group, single-blind, dose-ranging, phase 2 trial in PSAC (2–5 years) and school-aged children (SAC; aged 6–15 years) as a comparator group in southern Côte d'Ivoire. Children were randomly assigned (1:1:1:1) to 20 mg/kg, 40 mg/kg, or 60 mg/kg praziquantel or placebo. Participants, investigators, and laboratory technicians were masked to group assignment, while the investigator providing treatment was aware of the treatment group. The primary objective was to estimate the nature of the dose–response relation in terms of cure rate using the Kato Katz technique. Dose–response curves were estimated using Emax models. Available case analysis was done including all participants with primary endpoint data. This trial is registered with International Standard Randomised Controlled Trial, number ISRCTN15280205.
Findings
Between Nov 11, 2014, and Feb 18, 2015, 660 PSAC and 225 SAC were assessed for eligibility; of whom 161 (24%) PSAC and 180 (80%) SAC had a detectable Schistosoma mansoni infection. 161 PSAC were randomly allocated of whom 154 received treatment: 42 were assigned to 20 mg/kg praziquantel, of whom 40 received treatment; 38 were assigned to 40 mg/kg praziquantel, of whom 38 received treatment; 41 were assigned to 60 mg/kg praziquantel, of whom 39 received treatment; and 40 were assigned to placebo, of whom 37 received placebo. 180 SAC were randomly allocated of whom 177 received treatment: 49 were assigned to 20 mg/kg praziquantel, of whom 47 received treatment; 46 were assigned to 40 mg/kg praziquantel, of whom 46 received treatment; 42 were assigned to 60 mg/kg praziquantel, of whom 42 received treatment; and 43 were assigned to placebo, of whom 43 received treatment. Follow-up (available-case) data were available for 143 PSAC and 174 SAC. In PSAC, the 20 mg/kg dose resulted in cure in 23 children (62%; 95% CI 44·8–77·5), 40 mg/kg in 26 children (72%; 54·8–85·8), 60 mg/kg in 25 children (71%; 53·7–85·4), and placebo in 13 children (37%; 21·5–55·1). In SAC, the 20 mg/kg dose resulted in cure in 14 children (30%; 95% CI 17·7–45·8), 40 mg/kg in 31 children (69%; 53·4–81·8), 60 mg/kg in 34 children (83%; 67·9–92·8), and placebo in five children (12%; 4·0–25·6). For both age groups, the number of adverse events was similar among the three praziquantel treatment groups, with fewer adverse events observed in the placebo groups. The most common adverse events in PSAC were diarrhoea (11 [9%] of 124) and stomach ache (ten [8%]) and in SAC were diarrhoea (50 [28%] of 177), stomach ache (66 [37%]), and vomiting (26 [15%]) 3 h post treatment. No serious adverse events were reported.
Interpretation
Praziquantel shows a flat dose-response and overall lower efficacy in PSAC compared with in SAC. In the absence of treatment alternatives, a single dose of praziquantel of 40 mg/kg, recommended by the WHO for S mansoni infections in SAC can be endorsed for PSAC in preventive chemotherapy programmes.
Funding
European Research Council.
... Dose-response studies often presumes that there is a monotone relationship between administered doses and the observed response. However, the choice of an appropriate model to describe a biological process and the inference resulting from the parameter estimates is always associated with uncertainty regarding their suitability in capturing the underlying process (Briggs et al., 2012, Klingenberg, 2009). Traditionally, uncertainty in parameter estimates has been quantified by confidence (credible) intervals around a point estimate, which provide information about the accuracy of the estimates. ...
De Ziekte van Alzheimer (ZA) is een leeftijd gerelateerde aandoening die recent aan enorme belangstelling heeft gewonnen binnen de wetenschappelijke gemeenschap. De pathologische veranderingen, veroorzaakt door ZA, zijn onomkeerbaar en hebben een invloed op de kwaliteit-van-leven van de patiënt. Dit komt omdat ZA een impact heeft op zowel de motorische coördinatie als de cognitieve mogelijkheden van patiënten, waardoor deze afhankelijk worden van zorgverleners. De invloed van ZA op het welbevinden van patiënten wordt daarenboven vergroot omdat tijdige en accurate diagnose van de ziekte voorlopig ontbreekt. Daarom is huidig ZA onderzoek vooral gericht op de identificatie van biomerkers die zowel een accurate diagnose van ZA als de opvolging van de ziekte in termen van ziekteprogressie toelaten. Dit heeft als doel om de ontwikkeling van behandelingen, die de symptomen van ZA kunnen vertragen of zelfs voorkomen, te faciliteren. Om klinisch optimaal te zijn, dienen zulke biomerkers gemakkelijk en bij voorkeur non-invasief te bekomen zijn, om zodoende het ongemak van de patiënt tot een minimum te beperken. Daarnaast is het wenselijk dat zulke biomerkers pathologische ZA progressie accuraat kunnen voorstellen wanneer de ziekte zich nog in een vroeg stadium bevindt. Op dit moment kan de ware status van de ziekte pathologie enkel post-mortem worden vastgesteld. Dit is vruchteloos vanuit een patiëntbeheer standpunt.
... Later in this chapter, we illustrate some considerations involved in adaptive design methods using this approach. Further proposals include, among others, Hall et al. (2005), Weir et al. (2007), Ivanova et al. (2008), Klingenberg (2009) and Leonov and Miller (2009). ...
... Neal (2006) and Wakana et al. (2007) extended the original approach to Bayesian methods estimating or selecting the dose response curve from a sparse dose design. Klingenberg (2009) applied the MCP-Mod approach to proof-of-concept studies with binary responses. Benda (2010) proposed a time-dependent dose finding approach with repeated binary data. ...
We consider the problem of detecting a dose response signal if several competing
regression models are available to describe the dose response relationship. In particular,
we re-analyze the MCP-Mod approach from Bretz et al. (2005), which has become a
very popular tool for this problem in recent years. We propose an improvement based
on likelihood ratio tests and prove that in linear models this approach is always at least
as powerful as the MCP-Mod method. This result remains valid in nonlinear regression
models with identi able parameters. However, for many commonly used nonlinear dose
response models the regression parameters are not identi able and standard likelihood
ratio test theory is not applicable. We thus derive the asymptotic distribution of
likelihood ratio tests in regression models with a lack of identifiability and use this
result to simulate the quantiles based on Gaussian processes. The new method is
illustrated with a real data example and compared to the MCP-Mod procedure using
theoretical investigations as well as simulations.
The statistical methodology for model‐based dose finding under model uncertainty has attracted increasing attention in recent years. While the underlying principles are simple and easy to understand, developing and implementing an efficient approach for binary responses can be a formidable task in practice. Motivated by the statistical challenges encountered in a phase II dose finding study, we explore several key design and analysis issues related to the hybrid testing‐modeling approaches for binary responses. The issues include candidate model selection and specifications, optimal design and efficient sample size allocations, and, notably, the methods for dose‐response testing and estimation. Specifically, we consider a class of generalized linear models suited for the candidate set and establish D‐optimal designs for these models. Additionally, we propose using permutation‐based tests for dose‐response testing to avoid asymptotic normality assumptions typically required for contrast‐based tests. We perform trial simulations to enhance our understanding of these issues.
Background
Strongyloidiasis represents a major public health issue, particularly in resource-limited countries. Preliminary studies suggest that moxidectin might serve as an alternative to the only available treatment option, ivermectin. We aimed to evaluate the efficacy and safety of ascending doses of moxidectin in Strongyloides stercoralis-infected patients.
Methods
We did a randomised, parallel-group, single-blinded, placebo-controlled, dose-ranging, phase 2a trial in four villages in northern Laos. Eligible adults (aged 18–65 years) with S stercoralis infection intensities of at least 0·4 larvae per g of stool in at least two stool samples were randomly assigned (1:1:1:1:1:1:1) by use of computerised, stratified, block randomisation into seven treatment groups: 2 mg of moxidectin, 4 mg of moxidectin, 6 mg of moxidectin, 8 mg of moxidectin, 10 mg of moxidectin, 12 mg of moxidectin, or placebo. Participants and primary outcome assessors were masked to treatment allocation, but study site investigators were not. Participants received a single oral dose of their allocated dose of moxidectin in 2 mg tablets, or four placebo tablets. Three stool samples were collected at baseline and two stool samples were collected 28 days after treatment from each participant. A Baermann assay was used to quantify S stercoralis infection and Kato–Katz thick smears were used to qualitatively identify coinfections with additional helminths species. The primary endpoint was cure rate against S stercoralis and was analysed in an available case analysis set, defined as all randomly assigned participants with primary endpoint data. Predicted cure rates and associated CIs were estimated with hyperbolic Emax models. Safety was evaluated in the intention-to-treat population. This trial is registered at ClinicalTrials.gov, NCT04056325, and is complete.
Findings
Between Nov 27, 2019, and March 15, 2020, 785 adults were screened for trial eligibility. Of these, 223 participants were randomly assigned to treatment groups and 209 completed the study and were analysed for the primary outcome. 2 mg of moxidectin had a predicted cure rate of 75% (95% CI 59–87; 22 [73%] of 30 cured) against S stercoralis compared with a predicted cure rate of 14% (5–31; four [14%] of 29 cured) for placebo. With escalating doses, the probability of cure increased from 83% (95% CI 76–88; 26 [90%] of 29 cured) at 4 mg to 86% (79–90; 27 [84%] of 32 cured) at 6 mg, and to 87% (80–92; 24 [83%] of 29 cured) at 8 mg, levelling off at 88% (80–93; 29 [97%] of 30 cured) at 10 mg and 88% (80–93; 26 [87%] of 30 cured) at 12 mg. Moxidectin was well tolerated across all treatment groups, with no serious adverse events being recorded and all reported symptoms being classified as mild.
Interpretation
4–12 mg of moxidectin showed promising tolerability and efficacy profiles in the treatment of S stercoralis infections in adults. Because 8 mg of moxidectin is used for the treatment of onchocerciasis and has been evaluated for other helminth infections, we recommend this dose for phase 2b and phase 3 trials of strongyloidiasis therapy.
Funding
Fondazione Adiuvare.
In literature, there are a few unified approaches to test Proof-of-Concept and estimate a target dose, including the multiple comparison procedure using modeling approach, and the permutation approach proposed by Klingenberg. We discuss and compare the operating characteristics of these unified approaches and further develop an alternative approach in a Bayesian framework based on the posterior distribution of a penalized log-likelihood ratio test statistic. Our Bayesian approach is much more flexible to handle linear or non-linear
dose-response relationships and is more efficient than the permutation approach. The operating characteristics of our Bayesian approach are comparable to and sometimes better than both approaches in a wide range of dose-response relationships. It yields credible intervals as well as predictive distribution for the response rate at a specific dose level for the target dose estimation. Our Bayesian approach can be easily extended to continuous, categorical and time-to-event responses. We illustrate the performance of our proposed method with extensive simulations and Phase II clinical trial data examples.
Dose-response relationship study is an important factor for the new drug development program and it is the foundation to determine drug efficacy and safety. Through clinical trials, the study provide the basis for dosage regimen. However, the domestic studies pay little attention to dose-response relationship. Usually, only one fixed-dose or 2-3 dose groups are designed in clinical trial, dose-response study is ignored. This article focuses on the importance of the research, and reviews the experimental design and analysis methods in Phase II clinical trial.
We investigate likelihood ratio contrast tests for dose response signal detection under model uncertainty, when several competing regression models are available to describe the dose response relationship. The proposed approach uses the complete structure of the regression models, but does not require knowledge of the parameters of the competing models. Standard likelihood ratio test theory is applicable in linear models as well as in nonlinear regression models with identifiable parameters. However, for many commonly used nonlinear dose response models the regression parameters are not identifiable under the null hypothesis of no dose response and standard arguments cannot be used to obtain critical values. We thus derive the asymptotic distribution of likelihood ratio contrast tests in regression models with a lack of identifiability and use this result to simulate the quantiles based on Gaussian processes. The new method is illustrated with a real data example and compared to existing procedures using theoretical investigations as well as simulations.
© 2015, The International Biometric Society.
Understanding the dose-response relationship is a key objective in Phase II clinical development. Yet, designing a dose-ranging trial is a challenging task, as it requires identifying the therapeutic window and the shape of the dose-response curve for a new drug on the basis of a limited number of doses. Adaptive designs have been proposed as a solution to improve both quality and efficiency of Phase II trials as they give the possibility to select the dose to be tested as the trial goes. In this article, we present a 'shapebased' two-stage adaptive trial design where the doses to be tested in the second stage are determined based on the correlation observed between efficacy of the doses tested in the first stage and a set of pre-specified candidate dose-response profiles. At the end of the trial, the data are analyzed using the generalized MCP-Mod approach in order to account for model uncertainty. A simulation study shows that this approach gives more precise estimates of a desired target dose (e.g. ED70) than a single-stage (fixed-dose) design and performs as well as a two-stage D-optimal design. We present the results of an adaptive model-based dose-ranging trial in multiple sclerosis that motivated this research and was conducted using the presented methodology. Copyright © 2015 John Wiley & Sons, Ltd.
Copyright © 2015 John Wiley & Sons, Ltd.
We study the distributions of the LASSO, SCAD, and thresholding estimators, in finite samples and in the large-sample limit. The asymptotic distributions are derived for both the case where the estimators are tuned to perform consistent model selection and for the case where the estimators are tuned to perform conservative model selection. Our findings complement those of Knight and Fu [K. Knight, W. Fu, Asymptotics for lasso-type estimators, Annals of Statistics 28 (2000) 1356-1378] and Fan and Li [J. Fan, R. Li, Variable selection via non-concave penalized likelihood and its oracle properties, Journal of the American Statistical Association 96 (2001) 1348-1360]. We show that the distributions are typically highly non-normal regardless of how the estimator is tuned, and that this property persists in large samples. The uniform convergence rate of these estimators is also obtained, and is shown to be slower than n-1/2 in case the estimator is tuned to perform consistent model selection. An impossibility result regarding estimation of the estimators' distribution function is also provided.
The evolution of Bayesian approaches for model uncertainty over the past decade has been remarkable. Catalyzed by advances in methods and technology for posterior computation, the scope of these methods has widened substantially. Major thrusts of these developments have included new methods for semi-automatic prior specification and posterior exploration. To illustrate key aspects of this evolution, the highlights of some of these developments are described.
When testing for a treatment effect or a difference among groups, the distributional assumptions made about the response variable can have a critical impact on the conclusions drawn. For example, controversy has arisen over transformations of the response (Keene). An alternative approach is to use some member of the family of generalized linear models. However, this raises the issue of selecting the appropriate member, a problem of testing non-nested hypotheses. Standard model selection criteria, such as the Akaike information criterion (AIC), can be used to resolve problems. These procedures for comparing generalized linear models are applied to checking for difference in T4 cell counts between two disease groups. We conclude that appropriate model selection criteria should be specified in the protocol for any study, including clinical trials, in order that optimal inferences can be drawn about treatment differences. © 1998 John Wiley & Sons, Ltd.
Powers are compared of some tests of the equality of means in a one-way analysis of variance model with ordered alternative. The test statistics are: the likelihood ratio test, Williams's test and a modified Williams's test.
Various isotonic hypotheses are introduced in comparative clinical trials including a monotone dose-response relationship and its extension to two-way problems. Then a systematic approch for testing those hypothese based on the cumulative efficient scores is given with some applications to real data.
Motivated by the practical problem of analysing data from in vitro chromosome aberration assays this paper considers tests for differences between several proportions. Various test statistics are described, and the small sample behavior of tests which refer these statistics to approximating continuous distributions is investigated. The inaccuracies of these approximate tests can be avoided by using the exact conditional distribution of the test statistic. The calculation of the exact significance probability is described and the computation costs are shown to be negligible compared with the costs of data acquisition. Finally the use of the mid-P value is advocated for discretely distributed test statistics.
Single-Stage Procedures Two-Stage Procedures Incomplete Block Designs for Comparing Treatments with a Control
We argue that model selection uncertainty should be fully incorporated into statistical inference whenever estimation is sensitive to model choice and that choice is made with reference to the data. We consider different philosophies for achieving this goal and suggest strategies for data analysis. We illustrate our methods through three examples. The first is a Poisson regression of bird counts in which a choice is to be made between inclusion of one or both of two covariates. The second is a line transect data set for which different models yield substantially different estimates of abundance. The third is a simulated example in which truth is known.
Generalizations of Rao's score test are receiving increased attention, especially in the econometrics and biostatistics literature. These generalizations are able to account for certain model inadequacies or lack of knowledge by use of empirical variance estimates. This article shows how the various forms of the generalized test statistic arise from Taylor expansion of the estimating equations. The general estimating equations structure unifies a variety of applications and helps suggest new areas of application.
Several models with monotone trend in proportions are considered for 2 × I × J contingency tables. For one stratum (I = 1) and broad regularity conditions, the C(α) test statistic for testing for trend is shown to be fully efficient for all choices of the model with monotone trend. For several strata, the efficiency of each C(α) test is compared with the efficiency of the C(α) test appropriate when each of the other models holds. These relative efficiencies are used for choosing the most robust tests in a variety of sampling situations.
Developmental toxicity studies are designed to assess the potential adverse effects of an exposure on developing fetuses. Safe dose levels can be determined using dose-response modelling. To this end, it is important to investigate the effect of misspecifying the dose-response model on the safe dose. Since classical polynomial predictors are often of poor quality, there is a clear need for alternative specifications of the predictors, such as fractional polynomials. By means of simulations, we will show how fractional polynomial predictors may resolve possible model misspecifications and may thus yield more reliable estimates of the benchmark doses.
Powers are compared of some tests of the equality of means in a one-way analysis of variance model with ordered alternative. The test statistics are: the likelihood ratio test, Williams's test and a modified Williams's test.
The relationship between a response variable and one or more continuous covariates is often curved. Attempts to represent curvature in single- or multiple-regression models are usually made by means of polynomials of the covariates, typically quadratics. However, low order polynomials offer a limited family of shapes, and high order polynomials may fit poorly at the extreme values of the covariates. We propose an extended family of curves, which we call fractional polynomials, whose power terms are restricted to a small predefined set of integer and non-integer values. The powers are selected so that conventional polynomials are a subset of the family. Regression models using fractional polynomials of the covariates have appeared in the literature in an ad hoc fashion over a long period; we provide a unified description and a degree of formalization for them. They are shown to have considerable flexibility and are straightforward to fit using standard methods. We suggest an iterative algorithm for covariate selection and model fitting when several covariates are available. We give six examples of the use of fractional polynomial models in three types of regression analysis: normal errors, logistic and Cox regression. The examples all relate to medical data: fetal measurements, immunoglobulin concentrations in children, diabetes in children, infertility in women, myelomatosis (a type of leukaemia) and leg ulcers.
Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to over-confident inferences and decisions that are more risky than one thinks they are. Bayesian model averaging (BMA)provides a coherent mechanism for accounting for this model uncertainty. Several methods for implementing BMA have recently emerged. We discuss these methods and present a number of examples.In these examples, BMA provides improved out-of-sample predictive performance. We also provide a catalogue of currently available BMA software.
Dichotomous response models are common in many experimental settings. Statistical parameters of interest are typically the probabilities, pi, that an experimental unit will respond at the various treatment levels. Herein, simultaneous procedures are considered for multiple comparisons among these probabilities, with attention directed at construction of simultaneous confidence intervals for various functions of the pi. The inferences are based on the asymptotic normality of the maximum likelihood estimator of pi. Specific applications include all pairwise comparisons and comparisons with a fixed (control) treatment. Monte Carlo evaluations are undertaken to examine the small-sample properties of the various procedures. It is seen that use of the usual estimates of variance consistently leads to less-than-nominal empirical coverage for most sample sizes examined. For very large samples (total size greater than about 300), nominal coverage is achieved. A reformulation of the pairwise comparisons using a construction noted by Beal (1987, Biometrics 43, 941-950) is shown to exhibit generally nominal empirical coverage characteristics, and is recommended for use with small-to-moderate sample sizes.
The primary focus of this paper is to examine analysis strategies for parallel, randomized dose response studies with particular emphasis on identifying the minimum effective dose. Such studies have become a standard for drug development in the pharmaceutical industry. Particular attention is paid to ANOVA followed by multiple comparison procedures with some additional discussion of the utility or regression models. When there are three or fewer dose groups and a placebo in a study, ANOVA techniques are preferred; with a larger number of dose groups, regression analysis has greater utility and reliability. Analysis of factorial dose response studies is reviewed only slightly as this is an emerging area of interest, and further development is necessary.
A critical aspect of biomedical research is the characterization of the dose response relationship of a compound. This is true in laboratory experiments and clinical trials and pertains to efficacy, safety, and the resulting benefit/risk ratio. Presented here is Part I of this article, which deals with some clinical trial design issues surrounding dose response studies. Some additional comments are made about trials for identifying the minimum effective dose, randomized concentration controlled trials, and the use of one-sided hypotheses in designing such trials. Part II is a separate paper reviewing some analysis strategies for dose response studies.
When testing for a treatment effect or a difference among groups, the distributional assumptions made about the response variable can have a critical impact on the conclusions drawn. For example, controversy has arisen over transformations of the response (Keene). An alternative approach is to use some member of the family of generalized linear models. However, this raises the issue of selecting the appropriate member, a problem of testing non-nested hypotheses. Standard model selection criteria, such as the Akaike information criterion (AIC), can be used to resolve problems. These procedures for comparing generalized linear models are applied to checking for difference in T4 cell counts between two disease groups. We conclude that appropriate model selection criteria should be specified in the protocol for any study, including clinical trials, in order that optimal inferences can be drawn about treatment differences.
This paper presents a new test procedure for detecting trend in ordered 2 X K tables. Using an order-directed score statistic, the procedure does not require a set of scores preassigned to the ordinal categories under consideration. Thus the problem of varying p-values of linear rank tests, due to choices of different scoring systems, is avoided. The proposed test procedure can be easily generalized to handle stratified analysis where data are represented by several 2 x K tables. Examples are given to illustrate the method.
Recently, Stewart and Ruberg proposed the use of contrast tests for detecting dose-response relationships. They considered in particular bivariate contrasts for healing rates and gave several possibilities of defining adequate sets of coefficients. This paper extends their work in several directions. First, asymptotic power expressions for both single and multiple contrast tests are derived. Secondly, well known trend tests are rewritten as multiple contrast tests, thus alleviating the inherent problem of choosing adequate contrast coefficients. Thirdly, recent results on the efficient calculation of multivariate normal probabilities overcome the traditional simulation-based methods for the numerical computations. Modifications of the power formulae allow the calculation of sample sizes for given type I and II errors, the spontaneous rate, and the dose-response shape. Some numerical results of a power study for small to moderate sample sizes show that the nominal power is a reasonably good approximation to the actual power. An example from a clinical trial illustrates the practical use of the results.
Appropriate guidelines for clinical trials in irritable bowel syndrome are needed because of the inadequacy of previously performed trials, the use of new and more adequate patient definition, new emerging pathophysiological models and the unique requirements related to the assessment of treatment outcome that, in the absence of a biological marker, can rely only on the evaluation of clinical manifestations.
This consensus report highlights the following points.
(a) A 4-week period is considered to be adequate to assess drug efficacy for the control of symptoms.
(b) For the cyclic and non-life-threatening nature of the disease, a long-term study of 4–6 months or more of active treatment to establish efficacy is considered to be inappropriate in the large majority of patients.
(c) In the initial assessment phase of drug efficacy, the withdrawal effect of treatment can be ascertained during a follow-up period prolonged for a sufficient time (4–8 weeks) after stopping treatment. Subsequent trials with proper withdrawal phase design and duration can then ascertain the drug post-treatment benefit.
(d) Considering the intermittent clinical manifestations of irritable bowel syndrome, designing trials with on-demand or repeated cycles of treatment could be envisaged. However, the lack of a definition of what constitutes an exacerbation is a major obstacle to the design of such trials. In the absence of an established gold standard, appropriately justified novel trial designs are welcome.
(e) Patients eligible for inclusion should comply with the Rome II diagnostic criteria for irritable bowel syndrome.
(f) The main efficacy outcome of the treatment should be based on one primary end-point.
(g) The primary efficacy end-point could combine, in a global assessment, the key symptoms (abdominal pain, abdominal discomfort, bowel alterations) of irritable bowel syndrome or rate any single symptom for drugs considered to target specific symptoms.
(h) A 50% improvement in the primary efficacy end-point seems to be a reasonable definition of a responder.
The analysis of data from dose-response studies has long been divided according to two major strategies: multiple comparison procedures and model-based approaches. Model-based approaches assume a functional relationship between the response and the dose, taken as a quantitative factor, according to a prespecified parametric model. The fitted model is then used to estimate an adequate dose to achieve a desired response but the validity of its conclusions will highly depend on the correct choice of the a priori unknown dose-response model. Multiple comparison procedures regard the dose as a qualitative factor and make very few, if any, assumptions about the underlying dose-response model. The primary goal is often to identify the minimum effective dose that is statistically significant and produces a relevant biological effect. One approach is to evaluate the significance of contrasts between different dose levels, while preserving the family-wise error rate. Such procedures are relatively robust but inference is confined to the selection of the target dose among the dose levels under investigation. We describe a unified strategy to the analysis of data from dose-response studies which combines multiple comparison and modeling techniques. We assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying dose-response curve, while preserving the family-wise error rate. The selected model is then used to provide inference on adequate doses.
Since the National Food Safety Initiative of 1997, risk assessment has been an important issue in food safety areas. Microbial risk assessment is a systematic process for describing and quantifying a potential to cause adverse health effects associated with exposure to microorganisms. Various dose-response models for estimating microbial risks have been investigated. We have considered four two-parameter models and four three-parameter models in order to evaluate variability among the models for microbial risk assessment using infectivity and illness data from studies with human volunteers exposed to a variety of microbial pathogens. Model variability is measured in terms of estimated ED01s and ED10s, with the view that these effective dose levels correspond to the lower and upper limits of the 1% to 10% risk range generally recommended for establishing benchmark doses in risk assessment. Parameters of the statistical models are estimated using the maximum likelihood method. In this article a weighted average of effective dose estimates from eight two- and three-parameter dose-response models, with weights determined by the Kullback information criterion, is proposed to address model uncertainties in microbial risk assessment. The proposed procedures for incorporating model uncertainties and making inferences are illustrated with human infection/illness dose-response data sets.
The search for an adequate dose involves some of the most complex series of decisions to be made in developing a clinically viable product. Typically decisions based on such dose-finding studies reside in two domains: (i) "proof" of evidence that the treatment is effective and (ii) the need to choose dose(s) for further development. We consider a unified strategy for designing and analyzing dose-finding studies, including the testing of proof-of-concept and the selection of one or more doses to take into further development. The methodology combines the advantages of multiple comparisons and modeling approaches, consisting of a multi-stage procedure. Proof-of-concept is tested in the first stage, using multiple comparison methods to identify statistically significant contrasts corresponding to a set of candidate models. If proof-of-concept is established in the first stage, the best model is then used for dose selection in subsequent stages. This article describes and illustrates practical considerations related to the implementation of this methodology. We discuss how to determine sample sizes and perform power calculations based on the proof-of-concept step. A relevant topic in this context is how to obtain good prior values for the model parameters: different methods to translate prior clinical knowledge into parameter values are presented and discussed. In addition, different possibilities of performing sensitivity analyses to assess the consequences of misspecifying the true parameter values are introduced. All methods are illustrated by a real dose-response phase II study for an anti-anxiety compound.
Prediction of dose-response is important in dose selection in drug development. As the true dose-response shape is generally unknown, model selection is frequently used, and predictions based on the final selected model. Correctly assessing the quality of the predictions requires accounting for the uncertainties caused by the model selection process, which has been difficult. Recently, a new approach called data perturbation has emerged. It allows important predictive characteristics be computed while taking model selection into consideration. We study, through simulation, the performance of data perturbation in estimating standard error of parameter estimates and prediction errors. Data perturbation was found to give excellent prediction error estimates, although at times large Monte Carlo sizes were needed to obtain good standard error estimates. Overall, it is a useful tool to characterize uncertainties in dose-response predictions, with the potential of allowing more accurate dose selection in drug development. We also look at the influence of model selection on estimation bias. This leads to insights into candidate model choices that enable good dose-response prediction.
Quantitative risk assessment involves the determination of a safe level of exposure. Recent techniques use the estimated dose-response curve to estimate such a safe dose level. Although such methods have attractive features, a low-dose extrapolation is highly dependent on the model choice. Fractional polynomials, basically being a set of (generalized) linear models, are a nice extension of classical polynomials, providing the necessary flexibility to estimate the dose-response curve. Typically, one selects the best-fitting model in this set of polynomials and proceeds as if no model selection were carried out. We show that model averaging using a set of fractional polynomials reduces bias and has better precision in estimating a safe level of exposure (say, the benchmark dose), as compared to an estimator from the selected best model. To estimate a lower limit of this benchmark dose, an approximation of the variance of the model-averaged estimator, as proposed by Burnham and Anderson, can be used. However, this is a conservative method, often resulting in unrealistically low safe doses. Therefore, a bootstrap-based method to more accurately estimate the variance of the model averaged parameter is proposed.
An important component of quantitative risk assessment involves characterizing the dose-response relationship between an environmental exposure and adverse health outcome and then computing a benchmark dose, or the exposure level that yields a suitably low risk. This task is often complicated by model choice considerations, because risk estimates depend on the model parameters. We propose using Bayesian methods to address the problem of model selection and derive a model-averaged version of the benchmark dose. We illustrate the methods through application to data on arsenic-induced lung cancer from Taiwan.
The trend test of Williams is one of the most common approaches to test for monotone dose-response relationships. It has originally been introduced for one-way layouts. Applications of the Williams test beyond balanced block designs have not been described yet, what severely restricts its use in practice. An extension of Williams’ test to general unbalanced linear models is presented which allows the inclusion of covariates and/or factorial treatment structures. The test statistic of Williams is rewritten as the maximum of a finite number of standardized linear combinations of the means. The associated distribution function is seen to be available in closed form. Accordingly, p-values/critical values and power/sample sizes can be computed thoroughly. The methods are also applied to a modified version of Williams’ test. Data examples and numerical comparisons suggest a good performance of both extended approaches when compared to current competing methods.
Isotonic inference with particular interest in application to clinical trials Physica-Verlag: Heidelberg Copyright c ? Prepared using simauth
- C Hirotsu
- P Kitsos
- Edler
Hirotsu C. Isotonic inference with particular interest in application to clinical trials. In Industrial Statistics, Kitsos C P, Edler L (eds). Physica-Verlag: Heidelberg, 1997. Copyright c ? 2008 John Wiley & Sons, Ltd. Prepared using simauth.cls Statist. Med. 2008; 00:0–0 r18 B. KLINGENBER
Dose–response information to support drug registration
- Guidline
- Industry
Guidline for Industry. Dose–response information to support drug registration. Federal Register 1994; 59: 55972–55976.
Power (in %) of establishing PoC under dose-response model misspecification
- V Table
Table V. Power (in %) of establishing PoC under dose-response model misspecification, controlling the
FWER at 2.5% (except under the row labeled AIC).
- Hochberg